Lets have a Cournot oligopoly model. With two competitors, there is one Nash equilibrium. The thought experiment that can lead us to this result is for example the Tatonnement process, where there are infinitely many rounds and in each round one player takes opponents current output and uses it as a prediction for next round. It means that he takes opponents last action and in next round he plays the best response to it. This process converges to NE.
My question is as follows:
What is the connection of Strategic games and Stochastic games? Could the convergence process in our strategic game be seen as a play of infinite stochastic game, where states would be the production tuple from the previous round? The NE in strategic game would then be a tail of markov perfect equilibrium profile (ie players decide to remain in the same state for the rest of the game)
Could we for example justify Nash Equilibrium in strategic game as a result of learning to play the underlying stochastic game?
Sorry if my question is a bit chaotic. Any suggestions of reformulation are very welcome.